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When scaling psychological tests with methods of item response theory it is necessary to investigate to what extent the responses correspond to the model predictions. In addition to the statistical evaluation of item misfit, the question arises as to its practical significance. Although item removal is undesirable for several reasons, its practical consequences are rarely investigated and focus mostly on main survey data with pre-selected items. In this paper, we identify criteria to evaluate practical significance and discuss them with respect to various types of assessments and their particular purposes. We then demonstrate the practical consequences of item misfit using two data examples from the German PISA 2018 field trial study: one with cognitive data and one with non-cognitive/metacognitive data. For the former, we scale the data under the GPCM with and without the inclusion of misfitting items, and investigate how this influences the trait distribution and the allocation to reading competency levels. For non-cognitive/metacognitive data, we explore the effect of excluding misfitting items on estimated gender differences. Our results indicate minor practical consequences for person allocation and no changes in the estimated gender-difference effects. [ABSTRACT FROM AUTHOR]

Purpose: In Mokken scaling, the Crit index was proposed and is sometimes used as evidence (or lack thereof) of violations of some common model assumptions. The main goal of our study was twofold: To make the formulation of the Crit index explicit and accessible, and to investigate its distribution under various measurement conditions. Methods: We conducted two simulation studies in the context of dichotomously scored item responses. We manipulated the type of assumption violation, the proportion of violating items, sample size, and quality. False positive rates and power to detect assumption violations were our main outcome variables. Furthermore, we used the Crit coefficient in a Mokken scale analysis to a set of responses to the General Health Questionnaire (GHQ-12), a self-administered questionnaire for assessing current mental health. Results: We found that the false positive rates of Crit were close to the nominal rate in most conditions, and that power to detect misfit depended on the sample size, type of violation, and number of assumption-violating items. Overall, in small samples Crit lacked the power to detect misfit, and in larger samples power differed considerably depending on the type of violation and proportion of misfitting items. Furthermore, we also found in our empirical example that even in large samples the Crit index may fail to detect assumption violations. Discussion: Even in large samples, the Crit coefficient showed limited usefulness for detecting moderate and severe violations of monotonicity. Our findings are relevant to researchers and practitioners who use Mokken scaling for scale and questionnaire construction and revision. [ABSTRACT FROM AUTHOR]

Latent regression models are used for score-reporting purposes in large-scale educational survey assessments such as the National Assessment of Educational Progress (NAEP) and Trends in International Mathematics and Science Study (TIMSS). One component of these models is based on item response theory. While there exists some research on assessment of fit of item response theory models in the context of large-scale assessments, there is a scope of further research on the topic. We suggest two types of residuals to assess the fit of item response theory models in the context of large-scale assessments. The Type I error rates and power of the residuals are computed from simulated data. The residuals are computed using data from four NAEP assessments. Misfit was found for all data sets for both types of residuals, but the practical significance of the misfit was minimal. [ABSTRACT FROM AUTHOR]

The utility of Orlando and Thissen's (, ) S-X fit index was extended to the model-fit analysis of the graded response model (GRM). The performance of a modified S-X in assessing item-fit of the GRM was investigated in light of empirical Type I error rates and power with a simulation study having various conditions typically encountered in applied testing situations. The results show that the Type I error rates were controlled adequately around the nominal alpha by S-X. The power of the S-X statistic was much lower when the source of misfit was multidimensionality than when it was due to discrepancy from the true GRM curves. Once the data size increased sufficiently, however, appropriate power was obtained regardless of the source of the item-misfit. In summary, the generalized S-X appears to be a promising index for investigating item fit for polytomous items in educational and psychological assessments. [ABSTRACT FROM AUTHOR]